Question

Solve the following system of equations.

Answer 1

The answer is option A

Once you try substituting the values of options B and C, the equation is equal on both left and right hand sides hence the solutions is A

Answer 2

Answer:

Option A

A) (-3,-4) (4,3)

Step-by-step explanation:

We have a system of equations composed of:

The equation of a circle that has center at point (0,0) and radius r = 5.

The equation of a line that intercepts the y-axis at point (0,1)

To solve the system we substitute the equation of the line in the equation of the circumference:

$y = x - 1\\\\x ^ 2 + y ^ 2 = 25$

Then

$x ^ 2 + (x-1) ^ 2 = 25$

We solve for x.

$x ^ 2 + x ^ 2 -2x +1 = 25\\\\2x ^ 2 -2x -24 = 0$

We divide by 2 both sides of the equation

$x^2 -x -12 = 0$

We look for two numbers that multiply as a result -12 and that add them as a result -1.

These numbers are -4 and 3.

Therefore the factors are:

$(x-4) (x + 3) = 0$

Finally the solutions are:

$x = 4$ and $x = -3$

The ordered pairs are:

(-3,-4) (4,3)